I have never played the original (Or any for that matter) BioShock but have been tempted recently. Does it still hold up or does it look/play outdated now?

Absolutely, if anything the story in that game is still better then any campaigns today. That game was made back when developers didn't try and shoehorn MP in a game or mass produce games every year....people actually cared about what they were making, not how much they were going to make.